How do I set a mp4 as my background?
You can combine a 3D Scene with a video using different tools:

Node Editor (Compositing) 

PRO: Here you can apply filters, color correction, and other cool effects.

CONS: Non-linear editing is a little complicate

Some tips:


Set alpha mode Transparent in the Render Panel
Toggle Compositing in the Render Panel
Scale the Movie Clip to fit the render dimensions




VSE (Video Sequence Editor) 

PRO: Easy control over the timeline

CONS: Little effects

Some tips:


Select the Scene Strip and set Blend to Alpha Over
Toggle Sequencer in the Render Panel




This is only an overview: you'll find a lot of tutorial on the web about Node Compositing and VSE (Video Sequence Editor)